Design Wind Power Turbine - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 21

The.gearbox.in.a.wind.turbine.converts.the.slow,.high-torque.rotation.of.the.
turbine.into.a.much.faster.rotation.of.the.electrical.generator..These.are.much.
larger.and.more.complicated.than.the.PTO.gearboxes.in.farm.equipment..They.
weigh.several.tons.and.typically.contain.three.stages.to.achieve.an.overall.gear.
ratio.from.40:1.to.over.100:1,.depending.on.the.size.of.the.turbine..(For.aerody-
namic.and.structural.reasons,.larger.turbines.have.to.turn.more.slowly,.but.the.
generators.all.have.to.rotate.at.similar.speeds.of.several.thousand.rpm.).The.
irst.stage.of.the.gearbox.is.usually.a.planetary.gear,.for.compactness.and.to.
distribute.the.enormous.torque.of.the.turbine.over.more.teeth.of.the.low-speed.
shaft..Durability.of.these.gearboxes.has.been.a.serious.problem.for.a.long.time.

2.5 BladesDesign

Larger. rotors. with. longer. blades. sweep. a. greater. area,. which. increases.
energy. capture.. Simply. lengthening. a. blade. without. changing. the. funda-
mental. design,. however,. would. make. the. blade. much. heavier.. In. addition,.
the.blade.would.incur.greater.structural.loads.because.of.its.weight.and.lon-
ger.moment.arm..Using.advanced.materials.with.higher.strength-to-weight.
ratios.can.control.blade.weight.and.resultant.gravity-induced.loads..Because.
high-performance.materials,.such.as.carbon.ibers,.are.more.expensive,.they.
would.be.included.in.the.design.only.when.the.payoff.is.maximized..These.
innovative. airfoil. shapes. hold. the. promise. of. maintaining. excellent. power.
performance,. but. have. yet. to. be. demonstrated. in. full-scale. operation. (see.
Figure 2.1). 1 . This. airfoil. shape. keeps. a. basic. cutting. wind. load,. bending.
moments.relative.to.axis. x, y ,.and.twisting.moments..Here,.C.is.a.center.of.
acting. wind. forces.. We. have. assumed. that. the. power. turbine. blade. is. pre-
sented. as. a. curvature. plate. with. variable. thickness. and. force. acting. on. it..
Acting. forces. are. the. wind. load. F,. rotating. forces. on. angle.θ,. bending. and.
torsion.moments..Pagano.and.Soni 3 .assumed.that.the.blade.rotates.about.the.
x . axis,. which. is. parallel. to. X. with. a. constant. angular. velocity.. In. our. case,.
velocity.will.be.changed;.it.depends.on.the.strongest.winds..We.have.X,.Y,.Z.
Cartesian.coordinates.and.Polar.coordinates.R,.θ,.X..We.see.section.A-A.with.
acting.forces..Fz.is.an.axial.force.and.Fy.is.a.tangential.force..Mz.and.My.are.
bending.moments.and.Mx.is.a.rotating.moments.relative.to.axis.X.
The. area. of. cross. section. is. denoted. by. A. and. the. volume. of. the. region.
above.this.plane.by.V..ρ.is.designated.the.mass.density,.ω.the.angular.veloc-
ity,.r.=.radius.of.rotating.blade,.and.the.components.of.the.force.acting.on.the.
cross.section.A.are.given.by:

2 2

. Fz = ρω r sin r x dr d dx θ θ . (2.1)

v